Journal of Applied Mathematics and Stochastic Analysis
Volume 14 (2001), Issue 3, Pages 257-264
Invariant measures for Chebyshev maps
Concordia University, Department of Mathematics and Statistics, 7141 Sherbrooke Street, West Montreal H4B 1R6, Quebec, Canada
Received 1 April 2000; Revised 1 November 2000
Copyright © 2001 Abraham Boyarsky and Paweł Góra. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let , , where is not an integer.
For a certain set of 's which are irrational, the density of the unique absolutely continuous measure invariant under is determined exactly. This
is accomplished by showing that is differentially conjugate to a piecewise linear Markov map whose unique invariant density can be computed
as the unique left eigenvector of a matrix.